Transition energies of ytterbium, lutetium, and lawrencium by the relativistic coupled-cluster method

Rigorous Negative Ion Binding Energies in Low-Energy Electron Elastic Collisions with Heavy Multi-Electron Atoms and Fullerene Molecules: Validation of Electron Affinities

Dramatically sharp resonances manifesting stable negative ion formation characterize Regge pole-calculated low-energy electron elastic total cross sections (TCSs) of heavy multi-electron systems. The novelty of the Regge pole analysis is in the extraction of rigorous and unambiguous negative ion binding energies (BEs), corresponding to the measured electron affinities (EAs) of the investigated multi-electron systems. The measured EAs have engendered the crucial question: is the EA of multi-electron atoms and fullerene molecules identified with the BE of the attached electron in the ground, metastable or excited state of the formed negative ion during a collision? Inconsistencies in the meaning of the measured EAs are elucidated and new EA values for Bk, Cf, Fm, and Lr are presented.

Recent Progress in Low-Energy Electron Elastic-Collisions with Multi-Electron Atoms and Fullerene Molecules

We briefly review recent applications of the Regge pole analysis to low-energy 0.0 ≤ E ≤ 10.0 eV electron elastic collisions with large multi-electron atoms and fullerene molecules. We then conclude with a demonstration of the sensitivity of the Regge pole-calculated Ramsauer–Townsend minima and shape resonances to the electronic structure and dynamics of the Bk and Cf actinide atoms, and their first time ever use as novel and rigorous validation of the recent experimental observation that identified Cf as a transitional element in the actinide series (A. Müller, et al., Nat. Commun. 12, 948 (2021)).

Low-Energy Electron Elastic Collisions with Actinide Atoms Am, Cm, Bk, Es, No and Lr: Negative-Ion Formation

The rigorous Regge-pole method is used to investigate negative-ion formation in actinide atoms through electron elastic total cross sections (TCSs) calculation. The TCSs are found to be characterized generally by negative-ion formations, shape resonances and Ramsauer-Townsend(R-T) minima, and they exhibit both atomic and fullerene molecular behavior near the threshold. Additionally, a polarization-induced metastable cross section with a deep R-T minimum is identified near the threshold in the Am, Cm and Bk TCSs, which flips over to a shape resonance appearing very close to the threshold in the TCSs for Es, No and Lr. We attribute these new manifestations to size effects and orbital collapse significantly impacting the polarization interaction. From the TCSs unambiguous and reliable ground, metastable and excited states negative-ion binding energies (BEs) for Am−, Cm−, Bk−, Es−, No− and Lr− anions formed during the collisions are extracted and compared with existing electron affinities (EAs) of the atoms. The novelty of the Regge-pole approach is in the extraction of the negative-ion BEs from the TCSs. We conclude that the existing theoretical EAs of the actinide atoms and the recently measured EA of Th correspond to excited anionic BEs.

Electronic spectra of ytterbium fluoride from relativistic electronic structure calculations

We report an investigation of the low-lying excited states of the YbF molecule-a candidate molecule for experimental measurements of the electron electric dipole moment-with 2-component based multi-reference configuration interaction (MRCI), equation of motion coupled cluster (EOM-CCSD) and the extrapolated intermediate Hamiltonian Fock-space coupled cluster (XIHFS-CCSD). Specifically, we address the question of the nature of these low-lying states in terms of configurations containing filled or partially-filled Yb 4f shells. We show that while it does not appear possible to carry out calculations with both kinds of configurations contained in the same active space, reliable information can be extracted from different sectors of Fock space-that is, by performing electron attachment and detachment IHFS-CCSD and EOM-CCSD calculation on the closed-shell YbF+ and YbF- species, respectively. From these calculations we predict Ω = 1/2, 3/2 states, arising from the 4f13σ26s, 4f145d1/6p1, and 4f135d1σ16s configurations to be able to interact as they appear in the same energy range around the ground-state equilibrium geometry. As these states are generated from different sectors of Fock space, they are almost orthogonal and provide complementary descriptions of parts of the excited state manifold. To obtain a comprehensive picture, we introduce a simple adiabatization model to extract energies of interacting Ω = 1/2, 3/2 states that can be compared to experimental observations.

Assessment of the Second-Ionization Potential of Lawrencium: Investigating the End of the Actinide Series with a One-Atom-at-a-Time Gas-Phase Ion Chemistry Technique

Experiments were performed at the Lawrence Berkeley National Laboratory 88-Inch Cyclotron facility to investigate the electron-transfer reduction reaction of dipositive Lr (Z = 103) with O₂ gas. Ions of ²⁵⁵Lr were produced in the fusion-evaporation reaction ²⁰⁹Bi(⁴⁸Ca,2n) ²⁵⁵Lr and were studied with a novel gas-phase ion chemistry technique. The produced ²⁵⁵Lr²⁺ ions were trapped and O₂ gas was introduced, such that the charge-exchange reaction to reduce ²⁵⁵Lr²⁺ to ²⁵⁵Lr¹⁺ was observed and the reaction rate constant was determined to be k = 1.5(7) × 10^-10 cm³/mol/s. The observation that this reaction proceeds establishes the lower limit on the second ionization potential of Lr to be 13.3(3) eV. This gives further support that the actinide series terminates with Lr. Additionally, this result can be used to better interpret the situation concerning the placement of Lu and Lr on the periodic table within the current framework of the actinide hypothesis. The success of this experimental approach now identifies unique opportunities for future gas-phase reaction studies on actinide and super heavy elements.

Relativity and the periodic table

The periodic table provides a deep unifying principle for understanding chemical behaviour by relating the properties of different elements. For those belonging to the fifth and earlier rows, the observations concerning these properties and their interrelationships acquired a sound theoretical basis by the understanding of electronic behaviour provided by non-relativistic quantum mechanics. However, for elements of high nuclear charge, such as occur in the sixth and higher rows of the periodic table, the systematic behaviour explained by non-relativistic quantum mechanics begins to fail. These problems are resolved by realizing that relativistic quantum mechanics is required in heavy elements where electrons velocities can reach significant fractions of the velocity of light. An essentially non-mathematical description of relativistic quantum mechanics explains how relativity modifies valence electron behaviour in heavy elements. The direct relativistic effect, arising from the relativistic increase of the electron mass with velocity, contracts orbitals of low angular momentum, increasing their binding energies. The indirect relativistic effect causes valence orbitals of high angular momentum to be more effectively screened as a result of the relativistic contraction of the core orbitals. In the alkali and alkaline earths, the s orbital contractions reverse the chemical trends on descending these groups, with heavy elements becoming less reactive. For valence d and f electrons, the indirect relativistic effect enhances the reductions in their binding energies on descending the periodic table. The d electrons in the heavier coinage metals thus become more chemically active, which causes these elements to exhibit higher oxidation states. The indirect effect on d orbitals causes the chemistries of the sixth-row transition elements to differ significantly from the very similar behaviours of the fourth and fifth-row transition series. The relativistic destabilization of f orbitals causes lanthanides to be chemically similar, forming mainly ionic compounds in oxidation state three, while allowing the earlier actinides to show a richer range of chemical behaviour with several higher oxidation states. For the 7p series of elements, relativity divides the non-relativistic p shell of three degenerate orbitals into one of much lower energy with the energies of the remaining two being substantially increased. These orbitals have angular shapes and spin distributions so different from those of the non-relativistic ones that the ability of the 7p elements to form covalent bonds is greatly inhibited. This article is part of the theme issue 'Mendeleev and the periodic table'.

Low-Energy Electron Elastic Total Cross Sections for Ho, Er, Tm, Yb, Lu, and Hf Atoms

The robust Regge-pole methodology wherein is fully embedded the essential electron-electron correlation effects and the vital core polarization interaction has been used to explore negative ion formation in the large lanthanide Ho, Er, Tm, Yb, Lu, and Hf atoms through the electron elastic total cross sections (TCSs) calculations. These TCSs are characterized generally by dramatically sharp resonances manifesting ground, metastable, and excited negative ion formation during the collisions, Ramsauer-Townsend minima, and shape resonances. The novelty and generality of the Regge-pole approach is in the extraction of the negative ion binding energies (BEs) of complex heavy systems from the calculated electron TCSs. The extracted anionic BEs from the ground state TCSs for Ho, Er, Tm, Yb, Lu, and Hf atoms are 3.51 eV, 3.53 eV, 3.36 eV, 3.49 eV, 4.09 eV and 1.68 eV, respectively. The TCSs are presented and the extracted from the ground; metastable and excited anionic states BEs are compared with the available measured and/or calculated electron affinities. We conclude with a remark on the existing inconsistencies in the meaning of the electron affinity among the various measurements and/or calculations in the investigated atoms and make a recommendation to resolve the ambiguity.

Relativistic Effects on the Properties of Lr: A Periodic DFT Study of the Adsorption of Lr on Surfaces of Ta in Comparison with Lu and Tl

With the aim of finding out whether the predicted 7s²7p_1/2 ground-state electron configuration of Lr will have an effect on its reactivity, calculations of the adsorption properties of Lr(7s²7p), its homologue Lu(6s²5d), and the related p element Tl(6s²6p) on the surface of Ta were performed using the relativistic periodic ADF BAND suite. The obtained adsorption energies, E_ads(M), are in excellent agreement with the measured adsorption enthalpies of Lu and Tl, showing that Lr adsorbs on the surface of Ta similarly to Lu and much differently (215 kJ/mol more strongly) from Tl. An AO population analysis reveals that Lr interacts with the Ta surface preferentially via the 7s AO, with some participation of the 6d as well as 7p_1/2 and 7p_3/2 AOs. In contrast, E_ads(Tl) is governed mainly by the 6p(Tl) AOs. Thus, the present investigations show that Lr should behave like Lu but not like the p element Tl on transition-metal surfaces.

Relativity in the electronic structure of the heaviest elements and its influence on periodicities in properties

Theoretical chemical studies demonstrated crucial importance of relativistic effects in the physics and chemistry of superheavy elements (SHEs). Performed, with many of them, in a close link to the experimental research, those investigations have shown that relativistic effects determine periodicities in physical and chemical properties of the elements in the chemical groups and rows of the Periodic Table beyond the 6th one. They could, however, also lead to some deviations from the established trends, so that the predictive power of the Periodic Table in this area may be lost. Results of those studies are overviewed here, with comparison to the recent experimental investigations.

Four-Component Relativistic State-Specific Multireference Perturbation Theory with a Simplified Treatment of Static Correlation

The relativistic multireference (MR) perturbative approach is one of the most successful tools for the description of computationally demanding molecular systems of heavy elements. We present here the ground state dissociation energy surfaces, equilibrium bond lengths, harmonic frequencies, and dissociation energies of Ag₂, Cu₂, Au₂, and I₂ computed using the four-component (4c) relativistic spinors based state-specific MR perturbation theory (SSMRPT) with improved virtual orbital complete active space configuration interaction (IVO-CASCI) functions. The IVO-CASCI method is a simple, robust, useful and lower cost alternative to the complete active space self-consistent field approach for treating quasidegenerate situations. The redeeming features of the resulting method, termed as 4c-IVO-SSMRPT, lies in (i) manifestly size-extensivity, (ii) exemption from intruder problems, (iii) the freedom of convenient multipartitionings of the Hamiltonian, (iv) flexibility of the relaxed and unrelaxed descriptions of the reference coefficients, and (v) manageable cost/accuracy ratio. The present method delivers accurate descriptions of dissociation processes of heavy element systems. Close agreement with reference values has been found for the calculated molecular constants indicating that our 4c-IVOSSMRPT provides a robust and economic protocol for determining the structural properties for the ground state of heavy element molecules with eloquent MR character as it treats correlation and relativity on equal footing.

Is the chemistry of lawrencium peculiar?

The calculated properties of a set of simple model compounds are very similar for lawrencium and lutetium.

A Fock space coupled cluster study on the electronic structure of the UO2, UO2+, U4+, and U5+ species

The ground and excited states of the UO(2) molecule have been studied using a Dirac-Coulomb intermediate Hamiltonian Fock-space coupled cluster approach (DC-IHFSCC). This method is unique in describing dynamic and nondynamic correlation energies at relatively low computational cost. Spin-orbit coupling effects have been fully included by utilizing the four-component Dirac-Coulomb Hamiltonian from the outset. Complementary calculations on the ionized systems UO(2) (+) and UO(2) (2+) as well as on the ions U(4+) and U(5+) were performed to assess the accuracy of this method. The latter calculations improve upon previously published theoretical work. Our calculations confirm the assignment of the ground state of the UO(2) molecule as a (3)Phi(2u) state that arises from the 5f(1)7s(1) configuration. The first state from the 5f(2) configuration is found above 10,000 cm(-1), whereas the first state from the 5f(1)6d(1) configuration is found at 5,047 cm(-1).

Resonance transition energies and oscillator strengths in lutetium and lawrencium

The transition energies and oscillator strengths for nd (2)D(3/2)-(n+1)p (2)P(o)(1/2,3/2) transitions in Lu ( n = 5, Z = 71) and Lr ( n = 6, Z = 103) were calculated with the multiconfiguration Dirac-Hartree-Fock method. The present study confirmed that the ground state of atomic Lr is [Rn]5f(14)7s(2)7p (2)P(o)(1/2). The calculation for Lr required wave function expansions of more than 330 000 configuration states. In Lu, the transition energies, with Breit and QED corrections included, agree with experiment to within 126 cm(-1). In lighter elements, core correlation is usually neglected but was found to be of extreme importance for these heavy elements, affecting the oscillator strengths by a factor of 3 and 2 in Lu and Lr, respectively.

Measurement of the electron affinity of cerium

The electron affinity of cerium has been measured using laser photodetachment electron spectroscopy. The electron affinity of Ce(1G4) was determined to be 0.955 +/- 0.026 eV. The data also show that Ce- has at least two bound excited states with binding energies of 0.921 +/- 0.025 eV and 0.819 +/- 0.027 eV relative to the (1G4) ground state of the cerium atom. The present experimental measurements are compared to recent calculations of the energy levels of Ce-. Strong disagreement with the most recent theoretical atomic structure calculations highlights the complicated nature of this particular lanthanide.